College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.7 - Radical Expressions - R.7 Exercises - Page 68: 56



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the laws of radicals to simplify the given expression, $ \sqrt{\dfrac{5}{3p}} .$ Then rationalize the denominator. $\bf{\text{Solution Details:}}$ Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{\sqrt{5}}{\sqrt{3p}} .\end{array} Rationalizing the denominator results to \begin{array}{l}\require{cancel} \dfrac{\sqrt{5}}{\sqrt{3p}}\cdot\dfrac{\sqrt{3p}}{\sqrt{3p}} \\\\= \dfrac{\sqrt{5(3p)}}{(\sqrt{3p})^2} \text{ (product rule)} \\\\= \dfrac{\sqrt{15p}}{3p} .\end{array}
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